Are there any disadvantages to starting blender with the --enable-new-depsgraph argument?
You can watch and track any Dependency graph bugs here:

developer.blender.org > Dependency graph

All of the tickets look resolved now. There are no disadvantages that I know of.

However you never know if somewhere is a bug or not before you test it. If you work in a production environment you probably already test everything before you use it. If your tests are fine I would use --enable-new-depsgraph with ease in mind.